Nilpotent groups of semilinear transformations which are monomial
Keywords:
Nilpotent groups, Carter subgroupsAbstract
Let H be a nilpotent subgroup of ΓL_n (q) = <φ> GL_n (q), where φ denotes the field automorfism induced by the Frobenius map. We give a condition on the primes dividing |H ∩ GL_n (q)| under which H is conjugate to a subgroup of the generalized monomial group <φ> Diag_n (F∗_q ) Sym(n).We show an application of this result to the determination of Carter subgroups of finite groups.
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